"Define your terms!" It is the simplest advice for a philosopher or a scientist about to engage in debate. It ranks along with the truisms novices bear before they face their first audiences. Don't talk too fast. Make eye contact. It has an ancient pedigree. The sublime achievement of ancient science, Euclid's Elements, taught us what a perfectly formulated science looks like. It starts with definitions. "A point is..." "A line is..."

In my subspecialty of philosophy of physics, it is hard to imagine that this truism could cause trouble. We can define precisely which are the electrons and which the neutrinos. Until we do that we have little chance of speaking clearly about them.

That things might not be so simple is suggested by the example of "probability." The difficulties of providing a precise definition of the term are widely known. I've long abandoned any interest in the project. Whatever benefits it had have been outweighed by the harm of mighty inquisitors demanding a precise, even operational definition for the term. The project collapses into the pursuit of a misplaced doctrinal purity.

All this, I now learned, had played out as well in philosophy of biology. For today Yuichi Amitani is giving a Lunchtime Talk. He is a student of Soshichi Uchii, a celebrated past Fellow of the Center, and he went on to complete a PhD with John Beatty at the University of British Columbia on the species problem. Yuichi is spending the year with us as a Postdoctoral Fellow.

I knew that getting clear on just what species are had proven vexing, the stuff of heated, late nights. As the talk unfolded, it was clear that the vexation remained.

Yuichi began by reviewing old definitions. There is the idea that species are just morphologically distinct groups. There is the idea that species are just reproductively isolated groups. Both these straightforward definitions founder on counterexamples. Then there is the pluralist idea that there are many definitions, with different ones applied in different contexts.

All this was recapitulating what everyone in philosophy of biology knows, I presumed. It had the smell of decay. The idea of multiple definitions is a last ditched attempt to escape recalcitrant counterexamples. The danger of the escape is that you end up with a bag of definitions each of which, you soberly proclaim, work, except when they don't.

There was clearly a problem here, not in biology, but in our analyses. Yuichi went on to sharpen the problem. The biologists reason about species without difficulty. They may not have a text-book worthy definition but they proceed as if the term has a single meaning.

That tension--the failure of the definition project and successful use of the notion by biologists--set up the problem to be solved by the talk.

Yuichi's solution seemed to me to go in just the right direction. Give up the quest for a Euclidean definition. Instead, Yuichi will draw on work in cognitive science. There the notion of a prototype has been introduced. It is a highly exemplary instance of a concept. Once we know the prototype we can identify others merely by their resemblance to it. Or at least that is what I expect is the driving idea. I don't now recall that Yuichi explicitly said this.

photo by Christer Johansson

The remainder of the talk was devoted to developing this approach. His first step was to propose the notion of a "good species." These are cases that could function as the prototype. They satisfy many or most of the criteria one might have for a species and are recognized by naturalists as species.

By this stage of the talk, I began to notice the shift that had begun slowly but was now fully evident. The talk was developing many ideas from cognitive science. He called up the "dual process theory" of cognitive and social psychology. It identifies two facilities of understanding. One is implicit and unconscious. This Yuichi attached to prototype understanding, for that is our mode when we recognize things through prototypes. The other facility is explicit and conscious. This is our mode when we seek definitions, for they are difficult to find and we labor consciously to find them.

The talk proceeded in this way, shifting back and forth between species in biology and notions in psychology. I was following, but the details were getting ahead of me. Neither are my fields so it takes extra concentration to keep up. Instead, I was getting interested in an atavism of the talk. We routinely point at our slides with laser pointers. I had purchased a green laser, powerful enough to do eye surgery on the bored eyes in the back row, if I chose it.

In its place, Yuichi had a magnificent telescopic pointer with large red tip. It would have been our envy in the day when all self-respecting geeks carried a pen, a pencil and a pointer in their pockets.

The talk was now over. I chatted for a moment with Yuichi before someone from the audience came up. He began the rapid speech needed to convey an urgent message in the few moments between the end of the talk and start of question time.

It seemed to me that Yuichi's turn away from definitions to prototypes was the right move. What more could there be to say? What I'd forgotten was that this was an old debate. That means that everyone who has any acquaintance with the problem has a view. The exercise in listening to a talk is to see where the talk and your view differ, even if only in a crumb. That difference then becomes a banquet. Yuichi had, unwittingly, placed too much on the menu, for he had opened discussion not just of the species problem in biology but prototype theory and dual process theory in cognitive science.

This was a room with opinions and they were opinions on all this. Yuichi was about to discover them. Peter Machamer opened with the first question."Under the prototype theory," he demanded, "why isn't a whale a fish?"

My gaze dropped and my heart sank. This was a question asked more for rhetorical effect than to open useful discussion, for even I knew enough biology to see that the prototype approach could deal with that case. It might be difficult to sustain it in the quick repartee of question time with a quick witted questioner. The useful question would have asked about a real, but less theatrical, borderline case. Then Peter said something disparaging about dual process theory. I settled in to my job as referee.

We are scheduled to discuss Yuichi's ideas on species tomorrow in our reading group. There will be much to discuss. I might suggest that not all questions need to be answered with the full weight of Japanese politeness.